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OP-10193Status unassessedGeometry and topology

Categorical calculations · Question 3.3

Arborealization of singularities of Lagrangian skeleta · AIMPL workshop record

MSC 53D · Symplectic geometry, contact geometry

Editorial mapping of AIMPL list topic: Arborealization of singularities of Lagrangian skeleta. http://aimpl.org/arborlagrange/ Not an author-supplied MSC code.

Workshop record · status unassessedAs of 2026-09-10 source snapshot; not a current-status certificationSource & evidence ↓
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Problem statement

Can any smooth stable ∞\infty-category be realized as a finite colimit of categories associated to arboreal singularities? (This turns out to be true for tautological reasons, so we should demand further that such a colimit corresponds to a geometric gluing of the singularities.)

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Background

Workshop introduction

This page is intended to collect the problems arising from the AIM workshop, "Arborealization of singularities of Lagrangian skeleta."

Section context

For applications to mirror symmetry and representation theory, we are interested in better understanding the category of microlocal sheaves along an arboreal Lagrangian, both in specific cases of interest and in the abstract.

Question context

It is a well-known "fact" that "every category is a Fukaya category." Can the theory of arboreal spaces be used to give a proof of this assertion?

Progress & source assessment

Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.

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References
  1. [1]Arborealization of singularities of Lagrangian skeleta · Original question link
  2. [2]AIMPL source bibliography link
  3. [3]AIMPL text license · CC BY-SA 3.0 linkAIM Problem Lists (AIMPL), original contributors; CC BY-SA 3.0. Adaptation: structural TeX converted to Markdown, documented source macros expanded, and source bibliography links added. Mathematical wording retained. These adapted source texts remain under CC BY-SA 3.0.

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